Question

Find the smallest five digit number which is divisible by 12, 18 and 36

Answer 1

Given: Numbers 12, 18, 30.

To find: Here we have to find the smallest 5-digit number which is divisible by 12, 18, 30.

Solution:

Let us find LCM of 12, 18, 30.

12 = 2×2 ×3

18 = 2× 3²

30 = 2 × 3 × 5

Multiply each factor the greatest number of times it occurs in all numbers:

LCM = 2² ×3² ×5

LCM = 180.

If a number is divisible by 12, 18, 30. Then it should be a multiple of 180.

So we need to find the small 5-digit number which is a multiple of 180.

The smallest 5-digits number is 10000.

Let us divide it by 180.

We get a quotient 55 remainder is 100.

If we add 80 to it then it will be completely divided by 180 with a quotient 56.

Therefore,

180 × 56 = 10080

So, smallest 5-digits number divisible by 12, 15, and 18 is 10080.